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WEIGHTLESS

Why are astronauts in the International Space Station (ISS) weightless? “Because there is no gravity up there” you often hear. “Astronauts and scientists themselves often talk about zero-gravity, don’t they?”.

Weightless in space. Image credit: NASA A satellite orbit in its simplest form can be compared with uniform circular motion, like when you sling a weight around on a string. This circular motion requires a constant force towards the centre of the circle. For a satellite, including of course the ISS, gravity of the Earth provides that “centripetal” force. If there was no gravity up there, the ISS would take of in a tangential straight line and disappear into space because of Newton’s first law of motion.

So there definitely is gravity up there demonstrated by the fact that the ISS nicely continues to travel in its orbit. And this holds for any satellite, even the natural satellite we have: the Moon. She has been “up there” for at least 4 billion years.

Let us do some experiments.
When a skydiver jumps out of a plane at high altitude it is advisable to have a parachute, but keep that folded up for a while. She falls down at increasing speed and experiences weightlessness. A disturbing influence here is the wind and air drag she experiences. Astronauts don’t have that of course, but otherwise the situation is quite similar.

Modify the experiment by putting the skydiver in a box and dropping the whole box out of the plane (This is a thought experiment. DON’T DO THIS AT HOME). Now the skydiver will not feel any wind and will be almost weightless inside the box. Almost, because the box itself experiences the air drag and therefore falls a little slower than the skydiver. She will feel a very slight weight force towards the bottom (in the direction of falling).

Let us now look at a thought experiment that was proposed in 1687. Isaac Newton published his Philosophiæ Naturalis Principia Mathematica often just referred to as Principia, in which he explains his ground braking theory of gravity (among other things).

The image we show here of a canon on top of a mountain is from a later popularised version of the Principia. The idea is to fire the cannon, which is supposedly well above the atmosphere, with increasing charge and thus initial speed of the cannon ball. The latter will fall down to Earth at increasing distance, but there will be a speed at which the cannon ball will never hit the ground; it will continue to fall around the Earth. In practice this is impossible because of the Earth’s atmosphere and mountains that are not that tall, but as a thought experiment it is quite illustrative. As a matter of principle the cannon ball, orbiting the Earth will come back to the same spot where it left the cannon, therefore if this was possible, the gunner would himself be struck by the projectile he had fired a while ago.

Look at the animation of this experiment
Gradually increase the firing speed and see what happens. At which minimum speed will the cannon ball come back to point V in the diagram? (At higher speeds the cannon ball will disappear from Earth. We will come back to that below).

This experiment illustrates that a satellite orbit actually is a perpetual free fall in the gravity field of the central body, the Earth in our case. But, as Newton realised, this holds for all orbital motion in space, e.g. the motion of the Moon around the Earth and of the planets around the Sun.

So why are astronauts in the ISS weightless?
Because they are in a constant free fall motion around the Earth. And the space station itself and everything else in it is in that same free fall. The Earth’s gravity is the very reason they are moving that way. The term “zero-gravity” is therefore misleading. It is much more accurate to say “weightless” because while everything in orbit is accelerating in the direction of the Earth’s centre (like the cannon ball), there is no weight force like you would experience while standing on the surface of the Earth.

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